Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems

DOI10.3934/DCDS.2022120OpenAlexW4288364960MaRDI QIDQ2098852

Monique Dauge, Michael A. Hall, Ngọc San Vũ

Publication date: 22 November 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.10668

zbMATH Keywords

inverse problemquantizationrotation numberpseudodifferential operatorssemiclassical analysissymplectic invariantsLiouville integrable systemssemitoric systemsasymptotic latticegood labellinglattice detection

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geometry and quantization, symplectic methods (81S10) Pseudodifferential and Fourier integral operators on manifolds (58J40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Cites Work

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• Inverse spectral theory for semiclassical Jaynes-Cummings systems
• Diophantine tori and non-selfadjoint inverse spectral problems
• First steps in symplectic and spectral theory of integrable systems
• Equivariant inverse spectral theory and toric orbifolds
• Constructing integrable systems of semitoric type
• A geometric fractional monodromy theorem
• Birkhoff normal forms in semi-classical inverse problems.
• A brief introduction to Berezin-Toeplitz operators on compact Kähler manifolds
• Semitoric integrable systems on symplectic 4-manifolds
• Moment polytopes for symplectic manifolds with monodromy
• Almost toric symplectic four-manifolds
• Quasi-modes sur les variétés Riemanniennes
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. I: Le cas non intégrable
• Quantum monodromy in integrable systems
• Distribution of energy levels of a quantum free particle on a surface of revolution
• Semiclassical quantization rules near separatrices
• Clustering for the spectrum of \(h\)-pseudodifferential operators with periodic flow on an energy surface
• Faithful semitoric systems
• Rational invariant tori and band edge spectra for non-selfadjoint operators
• Integrable systems, symmetries, and quantization
• The inverse spectral problem for surfaces of revolution
• Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions. I
• Various quantum mechanical aspects of quadratic forms
• Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae
• Semi-global symplectic invariants of the spherical pendulum
• Monodromy, diabolic points, and angular momentum coupling
• Semiclassical inverse spectral theory for singularities of focus-focus type
• Symplectic geometry and spectral properties of classical and quantum coupled angular momenta
• Fractional monodromy: parallel transport of homology cycles
• A lecture on the classical KAM theorem
• Symplectic inverse spectral theory for pseudodifferential operators
• Symplectic theory of completely integrable Hamiltonian systems
• Spectra for Semiclassical Operators with Periodic Bicharacteristics in Dimension Two
• Diophantine tori and spectral asymptotics for nonselfadjoint operators
• The quantum mechanical spherical pendulum
• On global action-angle coordinates
• Periodic Hamiltonian flows on four-dimensional manifolds
• Quasimodes and Bohr-Sommerfeld Conditions for the Toeplitz Operators
• The affine invariant of proper semitoric integrable systems
• Passage through a potential barrier and multiple wells
• Singular Bohr–Sommerfeld rules for 2D integrable systems
• Inverse problems in spectral geometry
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Isospectrality for quantum toric integrable systems
• Spectral monodromy of non-self-adjoint operators
• Quantum monodromy and Bohr-Sommerfeld rules
• An introduction to semiclassical and microlocal analysis
• Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems

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